The algorithm of [1]} first computes several initial functions \(f\) 's, compute their smallest pre-feasible functions, and then take the join of them. Schrijver showed how to choose
such initial functions \(f\) 's so that the join of their smallest pre-feasible functions becomes a flow function corresponding to a \(T\) -linkage
homotopic to \(\mathcal {W}\) .
In Section REF , we will show that \(|\bar{f}(\cdot )|\)  has length \(2^{O(k)}\)  for all
functions \(\bar{f}\)  we consider in the course of the algorithm.
Therefore, to analyze the running time of this algorithm,
it suffices to analyze the number of functions \(f\) 's we compute.
